Analysis of Mode II and Mixed Mode I-II in Fracture and Fatigue: A Numerical and Experimental Study

  • J. Baganha Marques
  • S. M. O. TavaresEmail author
  • P. M. S. T. de Castro
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 98)


The aim of this work is to analyse fatigue crack propagation under pure mode II and mixed mode I-II loading conditions. Bidimensional numerical simulations were carried out using models created with the software Abaqus Standard, making use of the conventional finite element method to calculate the stress intensity factors and of the extended finite element method to predict the crack propagation path. The experimental tests were performed on single edge notch specimens, under asymmetrical four-point bending. By varying the position of supports and loads relatively to the crack several situations of mixed mode loading I-II and pure mode II were achieved. The equivalent stress intensity factor for mixed mode I-II and pure mode II was calculated using the finite element method and the software Abaqus Standard. The \(da/dN=f(\Delta K_{eq})\), where a is the crack length, N is the number o cycles, and \(\Delta K_{eq}\) is the range of the equivalent stress intensity factor, was obtained and compared with the mode I Paris law equation for the given material, NASGRO material database and other authors’ results. The initial fatigue crack growth (FCG) propagation angles were found to be well described by the minimum strain energy density criterion. Regarding the FCG rates, mixed mode results differ from mode I. Several factors like pre-existing flaws in the material, accumulation of experimental and/or post-processing errors and roughness-induced crack closure may have played a part in the differences obtained between the experimental material curve based on \(K_{eq}\) and the NASGRO and Paris law equations based upon \(K_{I}\). It is however noted that other authors also found some difference in the da / dN versus \(\Delta K_{eq}\) or versus \(\Delta K_{I}\) relationships. Finally, as regards cracks paths, xFEM predictions and experiments showed a variable degree of agreement: very good in some cases, and only approximate in others.


Fracture mechanics Fatigue Mixed mode loading I-II Mode II loading Extended finite element method 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • J. Baganha Marques
    • 1
  • S. M. O. Tavares
    • 1
    Email author
  • P. M. S. T. de Castro
    • 1
  1. 1.Faculdade de Engenharia da Universidade do PortoPortoPortugal

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